Composition law of cardinal order permutations

In this paper the theorems that determine composition laws for both cardinal ordering permutations and their inverses are proven. So, the relative positions of points in a hs-periodic orbit become completely known as well as in which order those points are visited. No matter how a hs-periodic orbit...

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Bibliographic Details
Published in:arXiv.org 2009-08
Main Authors: Jesus San Martin, Ma Jose Moscoso, A Gonzalez Gomez
Format: Article
Language:English
Subjects:
Bifurcations
Composition
Laws
Period doubling
Permutations
Online Access:Get full text
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Summary:In this paper the theorems that determine composition laws for both cardinal ordering permutations and their inverses are proven. So, the relative positions of points in a hs-periodic orbit become completely known as well as in which order those points are visited. No matter how a hs-periodic orbit emerges, be it through a period doubling cascade (s=2^n) of the h-periodic orbit, or as a primary window (like the saddle-node bifurcation cascade with h=2^n), or as a secondary window (the birth of a \(s-\)periodic window inside the h-periodic one). Certainly, period doubling cascade orbits are particular cases with h=2 and s=2^n. Both composition laws are also shown in algorithmic way for their easy use.
ISSN:2331-8422
DOI:10.48550/arxiv.0908.0065